论文标题
在$ \ mathrm {gu}（2,2）$上的Shimura品种的超大轨迹上
On the supersingular locus of the Shimura variety for $\mathrm{GU}(2,2)$ over a ramified prime
论文作者
论文摘要
我们研究了Rapoport的超大轨迹的结构 - 在$ \ mathrm {gu}（2,2）（2,2）$的Shimura Variety的Zink积分模型上，在分支的奇数上，具有特殊的最大脊髓降性水平。我们证明，超级基因座等于两个基本基因座的不相交联合，其中一个包含在平坦的基因座中，而另一个则不在。我们还明确描述了基本基因座的结构。更确切地说，前者纯粹是$ 2 $维的，并且每个不可约组件对Fermat表面都有主导地位。另一方面，后一个纯粹是$ 1 $维的，并且每个不可还原的组件对投影线都有主导地位。
We study the structure of the supersingular locus of the Rapoport--Zink integral model of the Shimura variety for $\mathrm{GU}(2,2)$ over a ramified odd prime with the special maximal parahoric level. We prove that the supersingular locus equals the disjoint union of two basic loci, one of which is contained in the flat locus, and the other is not. We also describe explicitly the structures of basic loci. More precisely, the former one is purely $2$-dimensional, and each irreducible component is birational to the Fermat surface. On the other hand, the latter one is purely $1$-dimensional, and each irreducible component is birational to the projective line.
